{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LeNet on Cifar\n",
    "\n",
    "This is LeNet (6c-16c-120-84) on Cifar10. Adam algorithm (lr=0.001) with 100 epoches.\n",
    "\n",
    "\n",
    "#### LeNet\n",
    "\n",
    "    Total params: 44,426\n",
    "    Trainable params: 44,426\n",
    "    Non-trainable params: 0\n",
    "\n",
    "\n",
    "####  LeNet with 10 intrinsic dim\n",
    "\n",
    "    Total params: 682,076\n",
    "    Trainable params: 10\n",
    "    Non-trainable params: 682,066\n",
    "    \n",
    "#### LeNet with 15000 intrinsic dim    \n",
    "    Total params: 930,167,006\n",
    "    Trainable params: 15,000\n",
    "    Non-trainable params: 930,152,006"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import *\n",
    "from decimal import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\" Extract final stats from resman's diary file\"\"\"\n",
    "def extract_num(lines0, is_reg=False):\n",
    "\n",
    "    if is_reg:\n",
    "        valid_loss_str     = lines0[-5]\n",
    "        valid_accuracy_str = lines0[-6]\n",
    "        train_loss_str     = lines0[-8]\n",
    "        train_accuracy_str = lines0[-9]\n",
    "        average_time_str   = lines0[-10]        \n",
    "        run_time_str       = lines0[-11]   \n",
    "        \n",
    "    else: \n",
    "        valid_loss_str     = lines0[-6]\n",
    "        valid_accuracy_str = lines0[-7]\n",
    "        train_loss_str     = lines0[-10]\n",
    "        train_accuracy_str = lines0[-11]\n",
    "        average_time_str   = lines0[-12]        \n",
    "        run_time_str       = lines0[-13]\n",
    "\n",
    "\n",
    "    valid_loss     = float(valid_loss_str.split( )[-1])\n",
    "    valid_accuracy = float(valid_accuracy_str.split( )[-1])\n",
    "    train_loss     = float(train_loss_str.split( )[-1])\n",
    "    train_accuracy = float(train_accuracy_str.split( )[-1])\n",
    "    run_time       = float(run_time_str.split( )[-1])\n",
    "    \n",
    "    return valid_loss, valid_accuracy, train_loss, train_accuracy, run_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "../results/fnn_cifar_l2_reg\n",
      "['0.01', '0.001', '0.0005', '0.0001', '0.00001', '0']\n"
     ]
    }
   ],
   "source": [
    "results_dir = '../results/fnn_cifar_l2_reg' \n",
    "print results_dir\n",
    "\n",
    "l2_value = [0.01,0.001,0.0005,0.0001,0.00001,0]\n",
    "dim = [0,250,500,750,1000,1250,1500,1750,1900,1950,2000,2050,2100,2250,2500,3000,4000,5000,5250,5500,5750,6000,6250,6500,6750,7000,7250,7500,7750,8000,8250,8500,8750,9000,9250,9500,9750,10000,15000,20000,25000,30000,35000,40000,45000,50000]\n",
    "\n",
    "\n",
    "l2_value_str = []\n",
    "for i in range(len(l2_value)):\n",
    "    if i<len(l2_value)-1:   \n",
    "        if i>2:\n",
    "            v = format(l2_value[i], '.'+str(i+2)+'f')[:-1] \n",
    "        else:\n",
    "            v = format(l2_value[i], '.'+str(i+2)+'f') \n",
    "    else:    \n",
    "        v = format(l2_value[i], '.'+str(0)+'f') \n",
    "    l2_value_str.append(v)\n",
    "    \n",
    "print l2_value_str\n",
    "\n",
    "# filename list of diary\n",
    "diary_names = []\n",
    "for subdir, dirs, files in os.walk(results_dir):\n",
    "    for file in files:\n",
    "        if file == 'diary':\n",
    "            fname = os.path.join(subdir, file)\n",
    "            diary_names.append(fname)\n",
    "# print diary_names\n",
    "          \n",
    "Rs = []    \n",
    "diary_names_ordered = []\n",
    "error_files = []\n",
    "\n",
    "for j in range(len(l2_value)):\n",
    "    l2 = l2_value[j]\n",
    "    for d in dim:\n",
    "        exist = False\n",
    "        for f in diary_names:\n",
    "            if '_'+str(d)+ '_2_200_'+l2_value_str[j]+'/' in f:\n",
    "                # print \"%d is in\" % d + f\n",
    "                exist = True\n",
    "                diary_names_ordered.append(f)        \n",
    "\n",
    "                with open(f,'r') as ff:\n",
    "                    lines0 = ff.readlines()\n",
    "                    try:\n",
    "                        R = extract_num(lines0, l2_value_str[j]=='0')\n",
    "                    except ValueError: \n",
    "                        error_files.append((l2,d))\n",
    "                        R = np.zeros(5)\n",
    "                        print \"Error. Can not read config: reg %.10f and dim %d.\" % (l2, d) \n",
    "\n",
    "                    # print \"%d dim:\\n\"%dim[i] + str(R) + \"\\n\"                \n",
    "\n",
    "                    Rs.append(R)\n",
    "        if exist == False:\n",
    "            print \"Missing: l2 \" + str(l2) + \", depth:\" +str(d)\n",
    "                                        \n",
    "Rs = np.array(Rs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 46, 5)\n",
      "[0, 250, 500, 750, 1000, 1250, 1500, 1750, 1900, 1950, 2000, 2050, 2100, 2250, 2500, 3000, 4000, 5000, 5250, 5500, 5750, 6000, 6250, 6500, 6750, 7000, 7250, 7500, 7750, 8000, 8250, 8500, 8750, 9000, 9250, 9500, 9750, 10000, 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000]\n",
      "[ 0.5045  0.2299  0.2932  0.3211  0.3519  0.3587  0.3759  0.3851  0.3835\n",
      "  0.3904  0.3935  0.3993  0.3981  0.3985  0.3984  0.4125  0.4305  0.4399\n",
      "  0.438   0.4463  0.4452  0.4478  0.4467  0.4528  0.4534  0.4607  0.4586\n",
      "  0.4537  0.4596  0.46    0.4622  0.4595  0.4662  0.4646  0.4618  0.4688\n",
      "  0.4687  0.4677  0.486   0.4902  0.4866  0.4906  0.4861  0.4826  0.4847\n",
      "  0.4883]\n",
      "[0, 0.5045],[250, 0.2299],[500, 0.2932],[750, 0.3211],[1000, 0.3519],[1250, 0.3587],[1500, 0.3759],[1750, 0.3851],[1900, 0.3835],[1950, 0.3904],[2000, 0.3935],[2050, 0.3993],[2100, 0.3981],[2250, 0.3985],[2500, 0.3984],[3000, 0.4125],[4000, 0.4305],[5000, 0.4399],[5250, 0.438],[5500, 0.4463],[5750, 0.4452],[6000, 0.4478],[6250, 0.4467],[6500, 0.4528],[6750, 0.4534],[7000, 0.4607],[7250, 0.4586],[7500, 0.4537],[7750, 0.4596],[8000, 0.46],[8250, 0.4622],[8500, 0.4595],[8750, 0.4662],[9000, 0.4646],[9250, 0.4618],[9500, 0.4688],[9750, 0.4687],[10000, 0.4677],[15000, 0.486],[20000, 0.4902],[25000, 0.4866],[30000, 0.4906],[35000, 0.4861],[40000, 0.4826],[45000, 0.4847],[50000, 0.4883]\n"
     ]
    }
   ],
   "source": [
    "Rs = Rs.reshape((len(l2_value), len(dim),5))\n",
    "print Rs.shape\n",
    "\n",
    "Test_Acc_e4 = Rs[-3,:,1]\n",
    "\n",
    "print dim\n",
    "print Test_Acc_e4\n",
    "\n",
    "print ','.join(['[%i, %s]' % (dim[n], Test_Acc_e4[n]) for n in xrange(len(dim))])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acc goal is: 0.4643 for L2 reg 0.01\n",
      "Acc goal is: 0.5379 for L2 reg 0.001\n",
      "Acc goal is: 0.5231 for L2 reg 0.0005\n",
      "Acc goal is: 0.5045 for L2 reg 0.0001\n",
      "Acc goal is: 0.5023 for L2 reg 1e-05\n",
      "Acc goal is: 0.4962 for L2 reg 0\n",
      "Intrinsic dim is: 50000.0 for network with L2_reg as 0.01\n",
      "Intrinsic dim is: 25000.0 for network with L2_reg as 0.001\n",
      "Intrinsic dim is: 15000.0 for network with L2_reg as 0.0005\n",
      "Intrinsic dim is: 7000.0 for network with L2_reg as 0.0001\n",
      "Intrinsic dim is: 6750.0 for network with L2_reg as 1e-05\n",
      "Intrinsic dim is: 5750.0 for network with L2_reg as 0\n"
     ]
    }
   ],
   "source": [
    "# 2.2 construct acc_solved_all and dim_solved_all \n",
    "\n",
    "acc_solved_all  = np.zeros(len(l2_value))\n",
    "dim_solved_all = np.ones(len(l2_value))*dim[-1]\n",
    "\n",
    "for i in range(len(l2_value)):\n",
    "    l2 = l2_value[i]\n",
    "    for j in range(len(dim)):\n",
    "        d = dim[j]\n",
    "        r = Rs[i,j,1]\n",
    "        if d==0:\n",
    "            test_acc_bl = r        \n",
    "            print \"Acc goal is: \" + str(test_acc_bl) + \" for L2 reg \" + str(l2)\n",
    "        else:\n",
    "            test_acc = r\n",
    "            if test_acc>test_acc_bl*0.90:\n",
    "                acc_solved_all[i]=test_acc\n",
    "                dim_solved_all[i]=d\n",
    "                break\n",
    "                \n",
    "for i in range(len(l2_value)):  \n",
    "    l2 = l2_value[i]\n",
    "    print \"Intrinsic dim is: \" + str(dim_solved_all[i]) + \" for network with L2_reg as \" + str(l2)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance comparison with Baseline\n",
    "\n",
    "\"Baseline method\" indicates optimization in the parameter space.\n",
    "\n",
    "The proposed method first embeds parameters into the intrinisic space (via orthogonal matrix), and optimization is the new space.\n",
    "\n",
    "The dimension of intrinsic space indicates the degree of freedom in the weights of neural nets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83d709450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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B8eee5vs4veXgBNkk4K1QFsoYY2orf+5p/sXjcwGwVVUzQ1QeY4yp1fwJmtuA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\nndZHZbzzP/oonHsuLFwIDz7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L/dyN0h0om3A6T6r9+wgM4HhHUJ2sB86UkTEenxcCQ2ry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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b5cfe50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4PKi5MMaENXd7o/v2eXfGbm56/ybe2/oe0fWiiwLjgeziLX+tG7WmS/MuXNHl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\nA9tc6y8B13mnA64DXvLY/5JrX2vgW4/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b5085d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mTJnCBx98wOrVq7n22mvza6h9+/YtNFxcp06dCgwXt3nzZrp160aHDh0YPXo0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b4b7550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Cst9XXnnF69NOgebL5fkQ93kRiQAq3hviTb6W7ljKsO+GsTBlIefWOZcpfafQ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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b3efd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DZtqM8YnjiakaQ/XK1ck8kUn6kXTc0zGICHHV4kp8vOKcSlvKkqLaERUVRaNGjahcuWQP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\n+MGCpjHG+MGCpjHG+MGCpjHG+OH/AaceQJiXKe4mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b384b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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h8bbFnMs8h181P1LTC1/krrIuJuHKmWJdgL3W2n3W2rPAIuC2AmUscEH2/SDg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\n4y7797+bWXes6KiXQLS2lVASrWWOV330+WMfqhoCROHVwH9mwGvBBdP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kmZJ/0Nxrm3Ui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\nJBz/D7p4hzfQUq9JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83b2c6f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_dir = 'figs/fnn_cifar_l2_reg/'\n",
    "directory = fig_dir\n",
    "if not os.path.exists(directory):\n",
    "    os.makedirs(directory)\n",
    "\n",
    "nn = len(dim)\n",
    "\n",
    "for i in range(len(l2_value)):\n",
    "    l2 = l2_value[i]\n",
    "    fig, ax = subplots(figsize=(5,4) )\n",
    "\n",
    "    plt.plot(dim[1:], Rs[i,1:,1], 'o-' , color=\"b\",  label=\"Testing\")\n",
    "    plt.plot(dim[1:], Rs[i,1:,3], 'o-' , color=\"g\",  label=\"Training\")\n",
    "    ax.plot(dim, Rs[i,0,1]*np.ones(nn)*0.9,'b-.', label=\"Testing: direct\")\n",
    "    ax.plot(dim, Rs[i,0,3]*np.ones(nn),'g-.', label=\"Training: direct\")\n",
    "\n",
    "    ax.set_xlabel('Intrinsic Dim.')\n",
    "    ax.set_ylabel('Accuracy')\n",
    "    plt.title('L2_Reg = '+str(l2))\n",
    "    plt.grid()\n",
    "    ax.legend()\n",
    "    ax.set_ylim([0.3,1.0])\n",
    "    # fig.savefig(\"figs/fnn_cifar_l2_reg/fnn_cifar_l2_reg_acc_\"+ str(l2) + \".pdf\", bbox_inches='tight')  \n",
    "\n",
    "# subplot style\n",
    "fig = plt.figure(figsize=(18,3))\n",
    "fig.subplots_adjust(left=0.05,right=0.95)\n",
    "\n",
    "for idx in range(len(l2_value)):\n",
    "        ax = plt.subplot(1, len(l2_value), idx+1)\n",
    "        \n",
    "        l2 = l2_value[idx]\n",
    "        plt.plot(dim[1:], Rs[idx,1:,1], 'o-' , color=\"b\",  label=\"Testing\")\n",
    "        plt.plot(dim[1:], Rs[idx,1:,3], 'o-' , color=\"g\",  label=\"Training\")\n",
    "        ax.plot(dim, Rs[idx,0,1]*np.ones(nn)*0.9,'b-.', label=\"Testing: direct\")\n",
    "        ax.plot(dim, Rs[idx,0,3]*np.ones(nn),'g-.', label=\"Training: direct\")\n",
    "\n",
    "        ax.set_xlabel('Intrinsic dim $d$')\n",
    "        \n",
    "        plt.title('L2_Reg = '+str(l2))\n",
    "        plt.grid()\n",
    "        ax.set_ylim([0.3,1.0]) \n",
    "        \n",
    "#         if idx > 0 and idx < 4:\n",
    "#             ax.set_ylim([0,3.1])\n",
    "#         elif idx > 3:\n",
    "#             ax.set_ylim([0,6.2])\n",
    "#         elif idx < 1:    \n",
    "#             ax.set_ylim([1,9.2])\n",
    "            \n",
    "        if idx == 0:\n",
    "            ax.set_ylabel('Accuracy')\n",
    "            ax.legend()\n",
    "        \n",
    "        \n",
    "fig.savefig(\"figs/fnn_cifar_l2_reg/fnn_cifar_l2_reg_acc_all.pdf\", bbox_inches='tight')          "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above figure show that updating in the intrinsic space can prevent overfitting.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xYk/6yspKLr30UrZs2VIjn+LiYu644w4+/PBDLrjgAibWbqyX3NxcPv30U0JC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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83d6f4390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Sv379cp8j6A0aIhIBzALuVNX9RXZ/B7RV1WwRuQJ4DzitjOdPBVIBYmNjWViG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83a8e2810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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G6Sg7NZviO4uZN3weEaFOBvIIroBhOcSep/fnSrV0GjQdZKdmM2vYLIIIrr0x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\nBU1jzGfAnjqSXAa8YmtO+BqIEZGOvsq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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83a86cfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Gpzm7PFHXhHWZa+bO9fqUVWbZsmVVnQWfCJZyGHNulyU725gvvjDmH/8wpn9/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\nSinlBQ2aSinlBQ2aSinlBQ2aSinlhf8PbZrw16RglNcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83a5e79d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3NwiAsLB8unc/ztq1oc5triIjTzN79k8+K7uvVedvJSkpabUxpux06aX4PCCK\nSAtgKZBqjJlXUdrExETj7qlo5R77qQCrZViagVkXGr/6j5Wenu7V0febN2/moosu8trxquLEiROE\nhITUSd7eVJf1KP3727PnbOvvhx+s84D2I1vo3h0uvxwuu8x67dTJagWWPIdoCQ72zS1vtak6fysi\n4lFA9Gm/QUSCgLlAWmXBsDpa0pbjVq+8dM6MeSPtnO82G2M8Gjqi6kZODuzbZ13lbdzYGrQcHg5F\nRYYzZ2DKlLNB0NH9DQ627u197DErAF56afldX8fXf8IEyMoyREcLqan+HQx9zZdXmQV4E9hsjPmX\nL/IYfdG9pG5+pmwrUcw5f8dK06ZNycnJITw8XINiPZSTY93R4ZjSKj/fmvXl118NeXk5LF/elDFj\n4PzzrVafowUYHw9VOf1ZG/f/NiS+bCFeDgwH1ouI48bRx40xX3grgwGRA0jdXM61/dDdpKWdu/8N\nO3TowN69ezl06FCt53369GmaNm1aecJ6ztv1KC62hrcUFFj38bo7W2UMFBY2pX37DmRlWQFR1R5f\nXmX+HvB50yQ8KMbtHSsgDH8hjXN19pugoCA6duxYJ3mnp6c7b1/zZ9WtR3a2dcXXddm0yToPWBkR\n9xOhqtrh92MPJt+ayrC5w912m81/3MOw5+GHH5KZPr1uyqf8T1qa47zb1URH4/a8mzHWeb3SQW/z\nZisgOjRrZk1rdeWV1owujuXGG91Pf++Pd3c0JH4fEJN7JDNs7jD3HwYWwS0pvPoZzAhIZtQoNDCq\nCrm7u+P++63JS9u0ORv0tmyxbl1zaNXKCnS33VYy8EVHW/f8lvbMMw3o7o4GxO8DIlTUbcaaIuyG\nMZj1ybz6Krz+Orzzzrl7blGVdfSodUEjM9Oaq6/0091OnwbH/AxRUVagGzmyZOBr06Zq8/mVvAJM\nuS1RVbsaRECcfGsq985PId/kuU8QnAM3PggLp1NYCMOGWcMZtLXof852Zz0PIrm5VrDbtcv969Gj\nlecrAkeOgH0LtFc0lLs7GpIGERCTe1jfqj/Mu4diisomEKDvqxCzFGZsBODVV2HOHJg8Wb+U/qL0\nQGPHw8rz863xeOUFvZycksdp1sx6jkdsrDWcJTb27PvbbnN/y1t0tHeDoaqfGkRAhLNBcdjcYe6v\nbQsQuQn+uxF88i6sTyYnx/qDAg2K9d2pU/DXv7p/WPm995bc1qSJNSVVx47Qp8/ZYOcIfOedV373\n9rnn9Nw0kHt8AAAVT0lEQVTeuazBBESwguKYhWPIOZXjPoFgXWgZPAw6/AALp5OXZ3XBoGxXzN02\nDZy+dfRoySu2jiUz0/24PYdZs84GvrZt3V/I8ITe3XFu89sJYssz+cbJSGXDHwXoOwN6WLNlOrpe\nu3dbf3S7d1snze+9t+S2YcOsSTIffBB9/KkbnkxGCtbPc/9++PZbmDYNHnrImn+vXTvrau1ll1lX\ndqdOtbqvffvCxInWhKXuxMRYAeuyy6B9++oHQ4fkZCsAf/vtUjIzNRieSxpUCxGsVuIPWT/w6qpX\nK04oBm67x1pfn1ymK+aYMLO03Fzr/KODI1AOH279oQcGWjfdi5Rs0YSHw+9/D198UV4rtPwxbzVV\nnQsR1cmj9HCVlBTrKWtdupRt9blO5NKypXWl9oYbrNe4OOs1NrbkFPSdO2t3VvlWgwuIANNvns7S\nzKVsyq5k6sXAIrjVPom4vmYRwhH8HDOQlO7e5eS4D6RnnQ0i4L2AVd6FCE/zKCqy9j15suyr6/q4\nce7P7z3yyNn3kZFWoLv77pKBr107z4as6FAV5WsNMiACbHxoI1EvRvFr7q8VJwzKI3DgBIpqGBC9\nJS/PGgtnP3a4RGCt6jrAs8+6D1SjRlnPxK0oyOXlwZkzNa/T999bgc8bD5vToSrKlxpsQATY95d9\nPPj5g5V2n4taZBHUJ42CKydYjzE9Fk3AklSK19bNX96RIyVbVr6Qmws//mh1OZs3t16jokq+d/da\n3mdXXul+uEpMjDW0RSl/0KADIljd5+k3TydtfRr3zL+HIuNmnCKGoltGAPbzFMN202hwCldeA9+8\nVPtBsUMH63GPDq7dSU/WXd936+Z+UoGYGOv5ut6iw1VUQ9DgA6KDY5xiymcp5BWc/att1qgZxhhO\nF5V8FnC+ySOj7RjC/2cCOQVWq5FvUmt8rrEyIlZw8dYg4GefrZ1ApcNVVEPQ4IbdVCS5RzIzb5lJ\nTGgMghATGsPrt77OmSL3J8pyTuVY90jbD7Bi8DCYKPDXCOiRVqV7Vz0hYp3b82YQSU62poyPibGO\nHxPjuynkdbiK8nfnVEAEKyhmjs2keGIxmWMzSe6RTHSoh3Muib00z4EhwzAThfDnI5i1Lo1Zs0oG\nnVmzrAscju1wdgiJayB1jJmLjDzN++/75v5qR6AqLkYDlVIVOOcCojup16YSHBRcrX1zTuUwbN4w\nRmWFkPpZWpmg4whG1kzI1mtx8dmn4xYVWa+zZ/+kgUqpOqYBEfdd6fBm4VU6Rm5+LsPmDUOeFuRp\nIeKFCNLW6y0sSvkTDYi20l1pj24BrICj5aiBUSn/oQGxHMk9khmVOKrGx3EERnlaCJwUiDwtxL4c\nq0FSqXpIA2IFpt88nVmDZ1W5+1yeYmM9PWj3sd1lguSdP92pQVKpOqYBsRLJPZLJfjQbM9FgJhpm\nDZ5F86DmXju+I0j+duY3hs8bzoOfP+i1YyulqkYDYhUl90gm9/Fcr7YcHQyGGatmaEtRqTqiAbGa\nXFuO3gyOBsNjix/zyrGUUlVzzty650vJPZKdtwYCHk0oUZE9x/cQPyOevu378ruo39E3qi8Xt7mY\nRgH661LKl/QvzAem3zydy6Mvr/hxBhUIbRJK+5D2zNsyjzfWvAFY91z3btebvlF9nUvHsI6It+8f\nVOocpgHRR0q3GgHS1qdVGiSDg4KZdvM0knskY4zhlyO/sGLfCmv5dQWvrnqVl36yHhIc3izcakG2\ntwLk76J+R5vmbcocM219GhO+mUDWsSyiQ6NJvTa1TNmUUhoQa1V5QbK8YCUidGrdiU6tO3FXj7sA\nKCgqYMPBDaz8daUzUP7Pzv9xXq2ODYu1gmN7q6u94/AORi8c7ZzhZ/ex3aR8luIsj1LqLA2IdcwR\nJNPT0+nfv3+l6YMCg+jVrhe92vUipY8V2HLzc/l5/8/OALl873LmbJxT7jHyCvKY8M0EDYhKlaIB\nsQFo0bgFV8VcxVUxVzm3HTx5kJX7VjLow0Fu99l9bDcjPhlB73a96d2uN/GR8YQ0CamtIitVL2lA\nbKDaNG/DzV1uJiY0ht3Hdpf5vGmjpizcsZB3174LgCBcGH6hFSDbWkGyV7tetG7mhQehKOUnNCA2\ncKnXppaZJTw4KJiZt8zk7ovvZn/ufn7e/zM/7/+ZNQfWsGzPMmZvmO1MGxMaYwXHtr2crcl2Ie3c\n5lXifGiGXrxR/sdnAVFE3gIGAQeNMRf7Kh9VMUdAKu/CTfuQ9rQPac+gLme71tl52azZv4Y1B9Y4\ng+X8LfOdn7dt0bZEgOzdrjc/ZP1AyoIUvXij/JovW4jvAFOB93yYh/KAu6vbFYkIjuC6TtdxXafr\nnNuOnznO2gNrnS3Jn/f/zFc7v3I+tCuAAIopLnGcvII8Hv/mcQ2Iym/4LCAaY/5PRGJ9dXxVu1o2\nacmVMVdyZcyVzm2nCk6x/uB61uxfw6jP3U+VlnUsi96v9aZLeBcubH0hF4Zf6HwNbxauA8tVvSKm\n9JPNvXlwKyAuqKjLLCIpQApAZGRkn9mzZ5eXtIzc3FxatGhRw1LWD/5elzt/upPfzvxWZnuzwGZc\n3PJi9p3ax4HTB0q0Ils0akGHZh2cS1SzKGs9uAMtGrn/WSz+bTFv7HqDg2cO0qZJG+7veD8DIgf4\npE7+/jtxda7XJSkpabUxJrGydHUeEF0lJiaaVatWeXx8T8fu+QN/r0va+rRyL944usz5RfnsOrKL\n7Ye3sz1nO9tytlnrh7ez59geDGe/ixHBEWdblXaLcnvOdlK/S+VU4aly8/Amf/+duDrX6yIiHgVE\nvcqsvKKyizcAjQMb0zWiK10jupbZ/3ThaXYe3sn2w3agzLEC5de/fO0cGuROXkEejyx6hKuir6JD\nyw7aBVc1ogFReU1V77px1bRRU7q36U73Nt3LfHYy/yQ7Du+g12u9SrQiHQ6ePEj0y9E0D2pOt4hu\nXHTeRVwUcZG1HnERnVt3JigwqLrVUucQXw67+RDoD0SIyF5gojHmTV/lpxqu5o2bE982nujQaLeD\nzCObRzLx6olsyd7C5uzNpGemM2vdLOfnjQIa0alVpzKBsltEN7d35+h4ynOXL68y3+WrY6tzU3mD\nzF8c+GKZgHXizAm25mxl86HNzkC5OXszC7YtoLC40JkuKiTKGSgviriIvcf38tJPLznPU+p4ynOL\ndpmV3/DkPKVDSJMQEtsnkti+5Hn0gqICdh7ZWSZQvp3xNrn5uW7zzSvIY8zCMUSFRHFBqwuICoki\nMCDQ+xVUdU4DovIrVR1kXlpQYBDdIrrRLaJbie3GGPad2Ef0S9Fuz1PmnMoh6d0k6xgBQcSExdAx\nrCMXtLrA+XpBqwvo2KojrZq28ujijs5TWf9oQFQKa+7JDi07lHuesn1Ie9697V12HdnFL0d+4Zej\nv7DryC4+3vRxmQl/Q5uE0rGVm2AZ1pGYsBiaNmpaZpiSds3rBw2ISrko7zzlC9e9wIAL3A8AP37m\nOLuO7GLXUTtYHvmFXUd3senQJj7f9jlnis440wpC+5D2ZOdll9gOeqtjfaABUSkXVTlP6dCySUvi\n28YT3za+zGfFppgDuQesIGm3Lncd3VXu2MqsY1l0n97dalWGXeBsXTq648FBwd6pqHJLA6JSpdRk\nPGVpARLgnFHoiugrnNvTM9Pdds1DGofQJbwLvxz5hfTM9DIXeiKbR5YIkq5L+5D2BEjJJwvrEKKq\n0YCoVB0or2v+6qBXnQHLGEPOqRxnN9x1+T7rez7c8KHzWTpg3Qnkes7yyKkjzN0819k11/OUldOA\nqFQd8KRrLiJEBEcQERxB36i+ZY6RX5RP1rEstwHzhz0/cPzM8TL75BXkcf+/72dp5lLOb3k+54ee\nT4eWHZzr53qXXAOiUnWkpkOIGgc2pnPrznRu3bnMZ8YYAicFuh1CdLrwNJ9s+YRDeYfKfNa6WWtn\ncDy/5fkl10PPJyokiiaNmpTZr6EMIdKAqFQDJCLlDiGKCY0hc2wmpwtPs+/4PvYc38OeY3tKvGYd\ny2LZnmUcPnW4zP5tmrcpESgPnTzEvC3zyC/KB/y7a64BUakGqrzzlKnXpgLWhBqO536X52T+SfYe\n31smaO49sZftOdv5dte35XbN7/v0Pr795VtiwmKIDYslJtR6jWoZRaOA+hl66meplFI1Vp0hRKU1\nb9y83CnbHAKeDnDbNT9TdIaFOxayP3d/ie2BEkiHlh2sIBkWQ2xo7Nn1sFg6tOxA48DGZY5XG1fM\nNSAq1YB5cwhReTzpmu85tofMo5nsPrabzKOZzvVvd33LvuP7SgRUQYhqGVWiVXngxAFmrZ/l8yvm\nGhCVUjXiSdf8wnBr1nN38ovy2Xt8rxUkj9oB85i1/n3W98zeMNv5MDNXeQV5TPhmggZEpVT9UdOu\neePAxs6xk+4UFhfS+O+N3XbLs45lVb/gbmhAVErVWE2HEFWkUUCjcrvl0aHRXs0roPIkSilVt1Kv\nTS0zaNy1W+4tGhCVUvVeco9kZt4yk5jQGAQhJjTGJ09b1C6zUsov1MYVc20hKqWUTQOiUkrZNCAq\npZRNA6JSStn8+qLK2IyxhGWGVZhmUJdBjLtsHAD93+nPiIQRjEgYQXZeNkPnDK00j9Lp/9LvL9zS\n9Ra2Zm/lgQUPVLp/6fTPXPsMl51/Gcv2LOPxbx53pjt69KjbupRO/9qg1+ga0ZXPtn7Giz++WGn+\npdN//PuPiQiO4J2Md3gn451K9y+dPn1EOgD/XPZPFmxb4HYf17q4pv9x74/M/f1cAB5b/Bg/7v2x\nwrzDg8NLpM85lcPMW2YCkPJZCttytlW4f5fwLiXShzcL59kBzwIwZM4QcvJyKtqdqOIo58n7IXOG\n0K9DvxLfpcrUp+/e2IyxTO803e13rzz19bvnS9pCVEopB2NMvVn69OljqmLJkiVVSl+faV3qn4ZS\nD2O0LsAq40EM0haiUkrZNCAqpZRNA6JSStk0ICqllE0DolJK2TQgKqWUTQOiUkrZNCAqpZRNrDGL\n9YOIHALKzhNevggg20fFqW1al/qnodQDtC4xxpjzKktUrwJiVYnIKmNMYl2Xwxu0LvVPQ6kHaF08\npV1mpZSyaUBUSimbvwfEmXVdAC/SutQ/DaUeoHXxiF+fQ1RKKW/y9xaiUkp5jQZEpZSy+W1AFJEb\nRGSriOwQkfF1XR4AEXlLRA6KyAaXba1F5GsR2W6/trK3i4hMscu/TkR6u+xzj51+u4jc47K9j4is\nt/eZIiLiw7qcLyJLRGSTiGwUkTH+Wh8RaSoiK0RkrV2Xp+3tHUVkuZ3/RyLS2N7exH6/w/481uVY\nj9nbt4rIQJfttfZ9FJFAEVkjIgv8vB6Z9u8/Q0RW2dvq9vvlySyy9W0BAoGdwAVAY2AtEFcPynUV\n0BvY4LLtBWC8vT4eeN5evwlYCAhwKbDc3t4a+MV+bWWvt7I/W2GnFXvfG31Yl3ZAb3s9BNgGxPlj\nfezjt7DXg4Dldr5zgDvt7TOAP9nrDwIz7PU7gY/s9Tj7u9YE6Gh/BwNr+/sIPAJ8ACyw3/trPTKB\niFLb6vT7VacBpAY/yH7AIpf3jwGP1XW57LLEUjIgbgXa2evtgK32+mvAXaXTAXcBr7lsf83e1g7Y\n4rK9RLpaqNenwHX+Xh8gGPgZuATrbodGpb9TwCKgn73eyE4npb9njnS1+X0EOgDfANcAC+xy+V09\n7ONnUjYg1un3y1+7zFHAHpf3e+1t9VGkMWa/vX4AiLTXy6tDRdv3utnuc3ZXqxdWy8ov62N3MzOA\ng8DXWC2ho8aYQjf5O8tsf34MCKfqdfSFl4FHgWL7fTj+WQ8AA3wlIqtFJMXeVqffL79+DKm/McYY\nEfGrcU4i0gKYC4w1xhx3PQ3jT/UxxhQBCSISBswHutVxkapMRAYBB40xq0Wkf12XxwuuMMbsE5E2\nwNcissX1w7r4fvlrC3EfcL7L+w72tvroNxFpB2C/HrS3l1eHirZ3cLPdZ0QkCCsYphlj5tmb/bY+\nAMaYo8ASrO5hmIg4GgWu+TvLbH8eCuRQ9Tp62+XArSKSCczG6jZP9sN6AGCM2We/HsT6J9WXuv5+\n+fqcjY/OPTTCOnnakbMnf7vXdbnsssVS8hziPyh5kvgFe/1mSp4kXmFvbw3swjpB3Mpeb21/Vvok\n8U0+rIcA7wEvl9rud/UBzgPC7PVmwHfAIOB/KXkx4kF7/SFKXoyYY693p+TFiF+wLkTU+vcR6M/Z\niyp+Vw+gORDisr4MuKGuv191HkBq8AO9CevK505gQl2Xxy7Th8B+oADrnMV9WOdsvgG2A4tdflkC\nTLPLvx5IdDnOvcAOexnpsj0R2GDvMxX7TiMf1eUKrHM864AMe7nJH+sD9ATW2HXZADxpb7/A/qPZ\nYQeVJvb2pvb7HfbnF7gca4Jd3q24XLWs7e8jJQOi39XDLvNae9noyKuuv196655SStn89RyiUkp5\nnQZEpZSyaUBUSimbBkSllLJpQFRKKZsGRFUtIpLrQZqxIhJcwedviEhcNfJOFJEpVUifbs/gsk5E\ntojIVPuOFcfny6paBtUw6bAbVS0ikmuMaVFJmkys8WJlHhkpIoHGup3O50QkHRhnjFllT431rF2u\nq2sjf+U/tIWoakRE+tstsI/t1leaPXfdw0B7YImILLHT5orIiyKyFuhn75fo8lmqWHMW/iQikfb2\n20Vkg739/1zydMwF2EJE3rbnvVsnIkMqKq8xJh9rcoRoEYl35O1y3KUi8qmI/CIiz4lIslhzKa4X\nkU4++SGqekMDovKGXsBYrHn2LgAuN8ZMAX4FkowxSXa65ljz2MUbY74vdYzmwE/GmHjg/4A/2tuf\nBAba2291k/d/A8eMMT2MMT2BbysrrN0yXYv7CR7igVHARcBwoIsxpi/wBjC6smMr/6YBUXnDCmPM\nXmNMMdYtfrHlpCvCmizCnXys+f0AVrsc4wfgHRH5I9b9tqUNwLqlCwBjzBEPy1ze7MkrjTH7jTFn\nsG75+srevp7y66UaCA2IyhvOuKwXUf60cqcrOG9YYM6e0HYewxgzCngCa0aT1SISXtPCikgg0APY\n7OZj17oUu7wvRqfLa/A0ICpfOoH1+IFqE5FOxpjlxpgngUOUnOoJrMleH3JJ36qS4wVhXVTZY4xZ\nV5OyqYZHA6LypZnAl46LKtX0D/uCxgasKaLWlvr8f4BWjgsvQFKZI1jSRMQx201z4D+qWyARuVVE\nJlV3f1V/6bAbpZSyaQtRKaVsGhCVUsqmAVEppWwaEJVSyqYBUSmlbBoQlVLKpgFRKaVs/w/RzfAd\n6YYenwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83ab474d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p6y6P9eutAFf13F5JiTWKu//+iuB30UXW9YPKhwHRGHMQOGi/PikiW4GugFcC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\nqwbNzbs3c/DkQZfXa4J1WH7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83ac1bfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Uo6z8DiggqMoY5dUk6AUS+BLdx819sqAmqPHKmiBjvRBCCJ+ilApTSkXY7gNX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\nEREREREREZFGQ8kuERERERERERFpNP4/J4rYJwyi1b8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83a9e9d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import MaxNLocator\n",
    "\n",
    "nn = len(dim)\n",
    "\n",
    "for i in range(len(l2_value)):\n",
    "    l2 = l2_value[i]\n",
    "    fig, ax = subplots(figsize=(5,4))\n",
    "\n",
    "    plt.plot(dim[1:], Rs[i,1:,0], 'o-' , color=\"b\",  label=\"Testing\")\n",
    "    plt.plot(dim[1:], Rs[i,1:,2], 'o-' , color=\"g\",  label=\"Training\")\n",
    "    ax.plot(dim, Rs[i,0,0]*np.ones(nn)*0.9,'b-.', label=\"Testing: direct\")\n",
    "    ax.plot(dim, Rs[i,0,2]*np.ones(nn),'g-.', label=\"Training: direct\")\n",
    "\n",
    "    ax.set_xlabel('Intrinsic Dim.')\n",
    "    ax.set_ylabel('NLL')\n",
    "    plt.title('L2_Reg = '+str(l2))\n",
    "    plt.grid()\n",
    "    ax.legend()\n",
    "    # ax.set_ylim([0.3,1.0])\n",
    "    # fig.savefig(\"figs/fnn_cifar_l2_reg/fnn_cifar_l2_reg_nll_\"+ str(l2) + \".pdf\", bbox_inches='tight') \n",
    "    \n",
    "    \n",
    "# subplot style\n",
    "fig = plt.figure(figsize=(18,3))\n",
    "fig.subplots_adjust(left=0.05,right=0.95)\n",
    "\n",
    "for idx in range(len(l2_value)):\n",
    "        ax = plt.subplot(1, len(l2_value), idx+1)\n",
    "        \n",
    "        l2 = l2_value[idx]\n",
    "        plt.plot(dim[1:], Rs[idx,1:,0], 'o-' , color=\"b\",  label=\"Testing\")\n",
    "        plt.plot(dim[1:], Rs[idx,1:,2], 'o-' , color=\"g\",  label=\"Training\")\n",
    "        ax.plot(dim, Rs[idx,0,0]*np.ones(nn)*0.9,'b-.', label=\"Testing: direct\")\n",
    "        ax.plot(dim, Rs[idx,0,2]*np.ones(nn),'g-.', label=\"Training: direct\")\n",
    "        \n",
    "        ax.set_xlabel('Intrinsic dim $d$')\n",
    "        \n",
    "        plt.title('L2_Reg = '+str(l2))\n",
    "        plt.grid()\n",
    "        ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "        \n",
    "        if idx > 0 and idx < 4:\n",
    "            ax.set_ylim([0,3.1])\n",
    "        elif idx > 3:\n",
    "            ax.set_ylim([0,6.2])\n",
    "        elif idx < 1:    \n",
    "            ax.set_ylim([1,9.2])\n",
    "            \n",
    "        if idx == 0:\n",
    "            ax.set_ylabel('NLL')\n",
    "            ax.legend()\n",
    "        \n",
    "fig.savefig(\"figs/fnn_cifar_l2_reg/fnn_cifar_l2_reg_nll_all.pdf\", bbox_inches='tight')        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above figure show that updating in the intrinsic space can prevent overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83d7289d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = subplots(figsize=(4,2) )\n",
    "\n",
    "ax.plot(l2_value, dim_solved_all,'ro-.')\n",
    "\n",
    "\n",
    "ax.set_xlabel('L2 Regularization')\n",
    "ax.set_ylabel('Intrinsic dim $d$')\n",
    "ax.set_xscale('log')\n",
    "# ax.set_xlim([0,0.012])\n",
    "plt.grid()\n",
    "\n",
    "fig.savefig(\"figs/fnn_cifar_l2_reg/fnn_cifar_l2_reg_intrinsic_dim.pdf\", bbox_inches='tight')    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
